improvements of the hydrological processes of the town

1

Improvements of the hydrological processes of the Town Energy

Balance Model (TEB-Veg, SURFEX v7.3) for urban modelling and

impact assessment

Xenia Stavropulos-Laffaille1, Katia Chancibault1, Jean-Marc Brun1, Aude Lemonsu2, Valery Masson2,

Aaron Boone2, Hervé Andrieu1 5

1IFSTTAR, GERS, EE, F-44344 Bouguenais, France 2CNRM UMR 3589, Météo-France/CNRS, Toulouse, 31057 Toulouse CEDEX 1, France

Correspondence to: Xenia Stavropulos-Laffaille ([email protected])

Abstract. Climate change and demographic pressure are common issues to be considered when conducting urban planning.

Local authorities and stakeholders have therefore opted for more nature-based adaptation strategies, which are especially 10

suitable to influence both hydrological and energy processes. Assessing the multiple benefits of such strategies on the urban

microclimate thus requires effective numerical tools. This paper presents recent developments of the water budget in the

TEB-Veg model (SURFEX v7.3), which allows for a better representation of the hydrological processes of urban subsoil.

This new hydrological module has been called TEB-Hydro. The developments studied concern the introduction of subsoil

underneath built surfaces, and the processes of: horizontally rebalancing intra-mesh soil moisture, draining soil water via the 15

sewer network, and limiting deep drainage in the aim of achieving a more realistic base flow pattern in the sewer system. A

sensitivity analysis is then performed in order to identify the hydrological parameters required for model calibration. The

new TEB-Hydro model is evaluated on two small residential catchments in Nantes (France) by comparing simulated sewer

discharges to observation findings. In both cases, the model tends to overestimate total sewer discharge and performs better

under wet climate conditions, with a KGE statistical criterion greater than 0.80 vs. roughly 0.60 under drier weather 20

conditions. Yet these findings remain encouraging since the same set of model parameters are identified for both catchments,

irrespective of meteorological and local physical conditions. This approach opens opportunities to apply the model at the city

scale with respect to projections of climate and demographic changes.

1. Introduction

Urbanisation is the predominant trend in today's world. Cities consume space and energy, generate pollution and nuisances, 25

and are vulnerable to natural or manmade hazards, such as floods and urban heat islands (hereafter denoted UHI), that

climate change is likely to exacerbate (EEA, 2012).

The adaptation of cities to global changes (climate change and demographic pressures) has become a major challenge in the

field of planning policy. The use of nature-based solutions (hereafter NBSs), such as green and blue infrastructure, has been

Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2018-39Manuscript under review for journal Geosci. Model Dev.Discussion started: 25 April 2018c© Author(s) 2018. CC BY 4.0 License.

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approved as part of sustainable urban development (Sustainable Urban Drainage Systems, water and pollution source

control, insulation of buildings) and is therefore recommended (Hamel et al., 2013; EC, 2015). However, evaluating such

adaptation and mitigation strategies requires conducting impact studies capable of assessing the various services these

solutions can offer along with their interactions (energy, thermal comfort, water, landscaping, etc.) (Bach et al., 2014). As

regards hydro-microclimatic patterns, the processes of evapotranspiration (or latent heat flux) constitute an increasingly 5

significant portion of both the urban water and energy budgets. For modelling purposes, evapotranspiration is thus a key

element since it affects the water and energy budgets (Mitchell et al., 2008).

Despite the increased interest in urban hydrology over recent years (Fletcher et al., 2013; Hamel et al., 2013; Shirmer et al.,

2013; Salvadore et al., 2015), the various water- and energy-related processes are still rarely addressed with the same level

of detail, and the coupling between them is often oversimplified. 10

In the past, the emphasis on the urban water cycle was directed at the design of urban drainage systems and their operations

under extreme events (flooding, low water level). Hydraulic models have thus been used to analyse rainfall-runoff patterns

during rain events when evapotranspiration is not a major concern (Berthier et al., 2006; Fletcher et al., 2013). In recent

decades however, a more decentralized urban water management system has necessitated impact studies that focus on the

urban water cycle as a whole. Consequently, urban hydrological models are being more heavily promoted, even though they 15

still simplify or neglect the energy balance. Evapotranspiration is therefore often calculated from a reference value of

potential evapotranspiration, which takes into account soil moisture conditions and sometimes vegetation (Rodriguez et al.,

2008; Rossman, 2010; DHI, 2001). At the local level, atmospheric demand is typically not considered a limiting factor for

evapotranspiration, and a direct interaction rarely exists between the water balance and the energy balance. In their state-of-

the-art paper, Fletcher et al. (2013) noted that evapotranspiration in urban areas remains relatively poorly explored. 20

Unlike hydrological models, the urban micro-climate models (Masson, 2000; Musy et al., 2015; Gros et al., 2016) provide a

detailed solution of energy and radiative budgets, while the water balance has been simplified, which can lead to an

alteration of the modelled latent heat fluxes (Grimmond et al., 2011). Malys et al. (2016) used such a model to evaluate the

mitigation effects of vegetation on UHI. Soil moisture however is not considered as a limiting factor, hence potentially

leading to an overestimation of the cooling abilities of plants, especially under hot climate conditions. For example, the 25

Town Energy Balance Scheme (TEB) described by Masson (2000) is a mesoscale surface scheme dedicated to the urban

environment. The urban environment is presented in a simplified manner by means of the street canyon approach (Oke,

1987), which averages the characteristics of urban covers and morphology (building height, construction materials, canyon

aspect ratio, street orientation) inside one grid mesh. This approach initially resolves detailed energy and radiative budgets of

built-up areas (buildings and roads), while the hydrological part is presented more simply, i.e.: i) artificial surfaces (buildings 30

and roads) are completely impervious; and ii) water exchanges are thus only taken into account between the surface and the

atmosphere. Lemonsu et al. (2007) then introduced the rainfall interception capacities of built-up surfaces and integrated

water infiltration through artificial surfaces, like roads, pavements and parking lots, into TEB in order to implement more

realistic hydrological processes. Using the ISBA-DF model (Interaction Soil-Biosphere-Atmosphere - explicit vertical


3

diffusion) (Boone et al., 2000) as part of the urban fabric, by integrating vegetated surfaces inside the street canyon, the TEB

model has evolved into TEB-Veg (Lemonsu et al., 2012). Interactions within the radiative, energy and water balances

between natural and artificial surfaces are now considered. Nevertheless, even if a detailed water balance for the subsoil of

natural surfaces is calculated, the water processes occurring in the subsoil of artificial surfaces and their interactions with the

surface are still neglected. 5

The objective of this study is to develop a complete urban hydro-microclimate model, hereafter called TEB-Hydro, by

integrating the subsoil under built-up surfaces and hydrological soil-surface interactions into the existing TEB-Veg model.

This step will allow treating the energy and water budgets at the same level of detail, which is critical to the impact

assessment of NBSs at a city scale. First, the model concept will be described. Since the energy and radiation components of

the model have not changed, as fully described in Masson (2000) and Lemonsu et al. (2012), the focus is placed on the 10

model's hydrological component and recent model developments. Next, the experimental sites and observation data will be

presented. The model evaluation will then be laid out in Section 4 in analysing the simulations performed by the new model

version.

2. Description of the TEB-Hydro hydrological model

TEB-Hydro is an evolution of TEB-Veg, with SURFEX v7.3 (Lemonsu et al., 2012), and was developed on the SURFEX 15

modelling platform (Masson et al., 2013). Like TEB-Veg, TEB-Hydro is based on a regular grid mesh and can be run either

coupled with other meteorological models or in offline mode forced by observed atmospheric data. It combines two surface

schemes, TEB (Masson, 2000) and ISBA-DF (Boone et al., 2000), both of which run on an integrated tiling approach and

describe energy and water exchanges between the urban and natural subsoils, the surface and atmosphere, respectively. The

urban environment is represented by three compartments, such as buildings (roofs and walls), roads (streets, pavements and 20

parking), and gardens. This section will present the new model developments based on the existing TEB-Veg model version.

A general description of the hydrological processes will be laid out first, followed by a discussion of the new developments

dedicated to hydrological processes in the urban subsoil (Fig. 1).

2.1 General principles of hydrological processes

Interactions between the energy balance (Eq. 1) and water balance (Eq. 2) are established via the explicit resolution of the 25

evapotranspiration term (Eq. 3):

𝑄∗ + 𝑄𝐹 = 𝑄𝐻 + 𝑄𝐸 + ∆𝑄𝑆 + ∆𝑄𝐴 [𝑊 𝑚−2] (1)

𝑃 + 𝐼 = 𝐸 + 𝑅 + 𝐷 + ∆𝑊 [𝑘𝑔 𝑚−2 𝑠−1] (2)

𝑄𝐸 =𝐸

𝐿𝑉 [𝑊 𝑚−2] (3)


4

where 𝑄∗ is the net all-wave radiation, 𝑄𝐹 the anthropogenic heat flux, 𝑄𝐻 the sensible heat flux, 𝑄𝐸 the latent heat flux, ∆𝑄𝑆

the heat flux storage, ∆𝑄𝐴 the net advection heat flux, 𝑃 the total precipitation, 𝐼 the water generated from anthropogenic

activities (irrigation), 𝐸 the evapotranspiration, 𝑅 the total runoff, 𝐷 the deep drainage, ∆𝑊 the variation in water storage

both on the surface and in the ground during the simulation period, and lastly 𝐿𝑣 the latent heat of vaporisation (-).

2.1.1 Evapotranspiration 5

The evaporation is calculated for each surface type 𝐸∗ (Fig. 1). For built-up surfaces, this value depends on both the surface

specific humidity at saturation and the air humidity (inside the canyon for roads and above the canopy level for roofs)

(Masson, 2000). Limitations are set by the maximum surface retention capacity of roofs 𝑊𝑚𝑎𝑥,𝑟𝑓𝑠𝑢𝑟𝑓

and roads 𝑊𝑚𝑎𝑥,𝑟𝑑𝑠𝑢𝑟𝑓

, as

represented by the surface water reservoirs. For natural surfaces, the various contributions from vegetation and natural

subsoil are considered (Eq. 4) (Lemonsu et al., 2012): 10

𝐸𝑔𝑑𝑛 = 𝐸𝑣𝑒𝑔 + 𝐸𝑔𝑟 + 𝐸𝑔𝑟,𝑖 + 𝐸𝑠 (4)

where Eveg is the vegetation evapotranspiration, Egr,i and Egr the evaporation from bare soil respectively with and without

freezing, and Es the sublimation from snow.

2.1.2 Water interception

The water content evolution in the interception water reservoirs of each surface type (denoted 𝑊∗𝑠𝑢𝑟𝑓

) is affected by 15

precipitation and evapotranspiration rates, as indicated in Masson (2000) and Lemonsu et al. (2012):

𝜕𝑊∗𝑠𝑢𝑟𝑓

𝜕𝑡= 𝑃 −

𝐸∗

𝐿𝑣 (5)

where * stands for rooftops, vegetation or bare ground surfaces.

For the road interception reservoir, the original evolution equation has been modified by including a slight water infiltration

rate (𝐼𝑟𝑑) (m s-1), since roads are never totally impervious (Ramier et al., 2011): 20

𝜕𝑊𝑟𝑑𝑠𝑢𝑟𝑓

𝜕𝑡= 𝑃 −

𝐸𝑟𝑑

𝐿𝑣− 𝐼𝑟𝑑 (6)

𝐼𝑟𝑑 is defined as a constant value over which the model must be calibrated.

2.1.3 Surface runoff

According to Masson (2000), when 𝑊∗𝑠𝑢𝑟𝑓

(mm) exceeds the maximum reservoir capacity (𝑊𝑚𝑎𝑥,∗𝑠𝑢𝑟𝑓

), surface runoff is

produced (𝑅∗𝑠𝑢𝑟𝑓

). Henceforth, it is collected by stormwater or combined sewer networks, depending on the connected 25

effective impervious areas fraction (𝑓𝑐𝑜𝑛) (Sutherland, 2000). Surface runoff not collected by the sewer system ((𝑅𝑟𝑓𝑠𝑢𝑟𝑓

+

𝑅𝑟𝑑𝑠𝑢𝑟𝑓

) ∗ (1 − 𝑓𝑐𝑜𝑛)) is then added to the throughfall over natural surfaces, where it can infiltrate into the subsoil with a


5

maximum infiltration capacity, according to the Green-Ampt approach (Abramopoulos et al., 1988; Entekhabi and Eagleson,

1989; Lemonsu et al., 2012).

The urban runoff 𝑅𝑡𝑜𝑤𝑛 (mm s-1), which is used to determine the total sewer discharge (𝑄𝑡𝑜𝑤𝑛𝑡𝑜𝑡 ), is composed of several

sources:

𝑅𝑡𝑜𝑤𝑛 = 𝑅𝑟𝑓𝑠𝑢𝑟𝑓

∗ 𝑓𝑐𝑜𝑛 + 𝑅𝑟𝑑𝑠𝑢𝑟𝑓

∗ 𝑓𝑐𝑜𝑛 + 𝑅𝑠𝑒𝑤 + 𝑅∗𝑠𝑢𝑏𝑠𝑢𝑟𝑓

(7) 5

where 𝑅𝑟𝑓𝑠𝑢𝑟𝑓

∗ 𝑓𝑐𝑜𝑛 and 𝑅𝑟𝑑𝑠𝑢𝑟𝑓

∗ 𝑓𝑐𝑜𝑛 are respectively the roof and the road surface runoff connected to the sewer network

(mm s-1); 𝑅𝑠𝑒𝑤 is the runoff in the sewer network due to soil water infiltration (mm s-1), and 𝑅∗𝑠𝑢𝑏𝑠𝑢𝑟𝑓

the subsurface runoff

from each compartment (mm s-1) calculated in Eq. 16.

2.1.4 Vertical water transfer

The surface water infiltration, as described above, constitutes an input to the subsoil of both the garden compartment and 10

road compartment. The water is then transferred vertically (𝑇𝑣) from layer to layer, accounting for the liquid water transfer

and water vapour transfer stated in Boone et al. (2000). This process depends solely on pressure gradients, which enables

taking different hydraulic soil properties into consideration. At the bottom of each soil column, the vertical water transfer is

adapted by taking boundary conditions into account. The resulting outgoing water flux of the model is called deep drainage

𝐷∗, which has been slightly modified for TEB-Hydro (Sect. 2.2.3). 15

2.2 Inclusion of hydrological processes in the urban subsoil

In accordance with the soil description of urban gardens provided in Lemonsu et al. (2012), soil compartments are now

considered under built-up surfaces such as roads and buildings. All three soil columns are represented by horizontal layers,

with an identical vertical grid in order to compute subsurface soil water transport. The thickness of each layer increases 20

downward, with a higher grid resolution on top. In the case of the road compartment, the upper soil layers are represented by

structural layers in accordance with Bouilloud et al. (2009). By integrating natural soil below urban surfaces, the

hydrological processes in the soil (vertical water transfer and deep drainage) of both road and building compartments are

being adapted from the garden compartment. Water infiltration through the road structure is thus now considered as a

recharge of soil moisture in the road compartment soil column. No water however is input into the building compartment soil 25

column.

2.2.1 Horizontal water transfer

The lateral water interactions of each soil layer among the three distinct compartments of a same grid cell have been added.

In considering the structural layers of the road compartment, the horizontal transfer in the upper soil layers is computed

solely between the garden and building compartments. Below there, all three compartments are accounted for. 30


6

This approach is based on the principle of an exponential decay of the water content, tending towards the mean soil moisture

of all three compartments, which is limited by soil moisture content at the wilting point. In assuming that the soil texture is

identical in each grid cell compartment and moreover that no lateral transfer is taking place between the various grid cells of

the model, the lateral intra-mesh soil moisture transfer for each soil layer is described as follows:

𝜕𝑊∗𝑔𝑟

𝜕𝑡= −

1

𝜏∗

𝐾𝑠𝑎𝑡̅̅ ̅̅ ̅̅ ̅

𝐾𝑖 (8) 5

Updating the soil moisture content in each layer and compartment after each time step yields:

𝑊∗𝑔𝑟,′

= 𝑊𝑔𝑟̅̅ ̅̅ ̅̅ + (𝑊∗𝑔𝑟

− 𝑊𝑔𝑟̅̅ ̅̅ ̅̅ ) ∗ 𝑒𝑥𝑝(− (1

𝜏∗

𝐾𝑠𝑎𝑡̅̅ ̅̅ ̅̅ ̅

𝐾𝑖) ∗ 𝑑𝑡) (9)

with: 𝑊𝑔𝑟̅̅ ̅̅ ̅̅ =∑ 𝑊∗

𝑔𝑟∗𝑓∗

∑ 𝑓∗ (10)

where 𝑊∗𝑔𝑟

and 𝑊∗𝑔𝑟,′

are respectively the soil moisture content for each compartment before and after horizontal balancing

(m3 m-3), 𝑊𝑔𝑟̅̅ ̅̅ ̅̅ the mean soil moisture content of all compartments before balancing (m3 m-3), 𝜏 the time constant of one day, 10

𝐾𝑠𝑎𝑡̅̅ ̅̅ ̅̅ ̅

𝐾𝑖 the ratio of the mean hydraulic conductivity at saturation of all three compartments to the hydraulic conductivity of each

compartment, 𝑑𝑡 the numerical time step of the model(s), and 𝑓∗ the fraction of each compartment.

2.2.2 Drainage of soil water by the sewer network

Various experiments and observations (Belhadj et al., 1995; Lerner, 2002; Berthier et al., 2004; Le Delliou et al., 2009) have

shown that soil water drainage occurs when artificial networks are situated under saturated soil moisture conditions. 15

However, the ISBA soil pattern is intended to depict the unsaturated zone rather than the saturated zone. This pattern is

based on a representation of the soil moisture state in agronomic terms (i.e. water content at wilting point, field capacity and

saturation). When taking this into account, the infiltration rate into the sewer network (𝐼𝑠𝑒𝑤 𝑖𝑛 m s-1) is described in such a

way that the hydraulic conductivity of the network soil layer (𝑘𝑠𝑒𝑤(𝑊𝑔𝑟) (m s-1)) is its limiting factor, with a maximum value

at saturation of: 20

𝐼𝑠𝑒𝑤 = 𝑘𝑠𝑒𝑤(𝑊𝑔𝑟) ∗ 𝐼𝑝 ∗ 𝐷𝑠𝑒𝑤 (11)

where 𝐼𝑝 is a calibration parameter, without any physical significance, representing the water tightness of the sewer pipe (-),

and 𝐷𝑠𝑒𝑤 the sewer density within a single grid cell (-) expressed by the ratio of the total sewer length in one grid cell (m) to

the maximum total sewer length in a single grid cell of the entire study site (m). Let's note that this formulation has been

adapted to TEB-Hydro from Rodriguez et al. (2008). 25

2.2.3 Deep drainage

In cities, artificial networks may play the role of rivers and thus contribute to draining soil water by means of infiltration. It

has therefore been envisaged to limit deep drainage in order to favour soil water infiltration into the sewer networks during


7

wet periods. For this purpose, the soil moisture emerging from the last layer of the model is partially or totally retained,

according to a coefficient 𝐶𝑟𝑒𝑐ℎ, until complete layer saturation. At each time step, the soil moisture content in the last layer

n is thus updated according to:

𝑊∗𝑔𝑟,𝑛

= 𝑊∗𝑔𝑟,𝑛

+ 𝑊∗𝑔𝑟,𝑓𝑙𝑢𝑥,𝑛

∗ 𝐶𝑟𝑒𝑐ℎ (12)

And the deep drainage becomes: 𝐷∗ = 𝑊∗𝑔𝑟,𝑓𝑙𝑢𝑥,𝑛

∗ (1 − 𝐶𝑟𝑒𝑐ℎ) ∗ 𝑑𝑛 ∗ 𝜌/𝑑𝑡 (13) 5

where 𝑊∗ 𝑔𝑟,𝑛

is the soil moisture content of the last layer n (m3 m-3), 𝑊∗𝑔𝑟,𝑓𝑙𝑢𝑥,𝑛

the soil moisture content derived from the

outgoing water flux (m3 m-3), 𝐶𝑟𝑒𝑐ℎ the coefficient of retention (-), 𝐷∗ the deep drainage (mm s-1), 𝑑𝑛 the thickness of the last

layer, 𝜌 the water density (kg m-3), and dt the numerical time step of the model(s).

If the deep layer is saturated, the excess moisture rises from layer to layer, with:

The soil moisture content in upper layer i-1: 𝑊∗𝑔𝑟,𝑖−1,′

= 𝑊∗ 𝑔𝑟,𝑖−1

+ max(0 , 𝑊∗𝑔𝑟,𝑖

− 𝑊∗,𝑠𝑎𝑡𝑔𝑟,𝑖

) ∗𝑑𝑖−1

𝑑𝑖 (14) 10

The soil moisture content remaining in layer i: 𝑊∗𝑔𝑟,𝑖,′

= min( 𝑊∗𝑔𝑟,𝑖

, 𝑊∗,𝑠𝑎𝑡𝑔𝑟,𝑖

) (15)

If saturation reaches the surface layer, then the excess moisture is added to subsurface runoff:

𝑅∗𝑠𝑢𝑏𝑠𝑢𝑟𝑓,′

= 𝑅∗𝑠𝑢𝑏𝑠𝑢𝑟𝑓

+ max(0 , 𝑊∗𝑔𝑟,1

− 𝑊∗,𝑠𝑎𝑡𝑔𝑟,1

) ∗𝑑1

𝑑𝑡∗ 𝜌 (16)

where 𝑊∗,𝑠𝑎𝑡𝑔𝑟,𝑖

is the soil moisture content at saturation (m3 m-3), 𝑊∗𝑔𝑟,𝑖,′

and 𝑊∗ 𝑔𝑟,𝑖

respectively the soil moisture content in 15

current layer i, after and before update (m3 m-3), 𝑊∗𝑔𝑟,𝑖−1,′

and 𝑊∗ 𝑔𝑟,𝑖−1

respectively the soil moisture content in upper soil

layer i-1, after and before update (m3 m-3), 𝑑𝑖−1

𝑑𝑖 (-) the ratio of layer thicknesses between upper layer i-1 and lower layer i,

and 𝑅∗𝑠𝑢𝑏𝑠𝑢𝑟𝑓,′

and 𝑅∗𝑠𝑢𝑏𝑠𝑢𝑟𝑓

respectively the subsurface runoff after and before update (mm s-1).

2.3 TEB-Hydro output variables

In addition to the simulated hydrological output variables calculated in TEB-Veg (latent heat fluxes on all surfaces, soil 20

moisture in each soil layer (𝑊𝑔𝑑𝑛𝑔𝑟,𝑖

) and deep drainage (𝐷𝑔𝑑𝑛) of the garden compartment), the TEB-Hydro model simulates

the soil moisture in each soil layer (𝑊∗𝑔𝑟,𝑖

) and the deep drainage (𝐷∗) under artificial surfaces. Other new model output

variables include urban runoff (𝑅𝑡𝑜𝑤𝑛 ), with its components stemming from rooftops (𝑅𝑟𝑓𝑠𝑢𝑟𝑓

∗ 𝑓𝑐𝑜𝑛 ) and road surfaces

(𝑅𝑟𝑑𝑠𝑢𝑟𝑓

∗ 𝑓𝑐𝑜𝑛), soil water infiltration into the sewer network (𝑅𝑠𝑒𝑤 ), and the subsurface runoff from each compartment

(𝑅∗𝑠𝑢𝑏𝑠𝑢𝑟𝑓

). 25


8

3. Experimental study areas and observation data

The experimental data are derived from two small urban catchments in the city of Nantes (France). The properties of these

catchments, along with local observation data and the meteorological forcing data of the model will be described below.

3.1 Experimental data

3.1.1 Rezé catchment 5

The Rezé experimental site is located in the southern part of the city of Nantes, close to the Atlantic coast (Fig. 2). It was

instrumented (with measurements of precipitation, discharge from the rainwater network and soil water) from 1993 to 1998,

and a complete continuous database is available for that period. The climate is oceanic with an average annual rainfall of

approx. 830 mm during this period; the year 1994 was the wettest one.

The 4.7-ha basin is entirely residential, comprising single-family homes with private gardens. The separate sewer network is 10

divided into wastewater and stormwater with lengths of 803 m and 480 m, respectively. The impervious surface of the

catchment accounts for 45% of the total area, of which 84% is connected to the stormwater system. A detailed site

description can be found in Berthier et al. (1999) and Dupont et al. (2006) (Tab. 1).

The Rezé catchment and its database have been the subject of several studies (Rodriguez et al., 2003; Berthier et al., 2004;

Dupont et al. (2006); Lemonsu et al., 2007; Rodriguez et al., 2008). Berthier (1999) modelled the role of soil in generating 15

urban runoff on the Rezé catchment. He studied both the hydrological aspects and site observations. Among other emphases,

he examined the discharge observed in the wastewater sewer during the winter periods between 1993 and 1997 before

estimating the discharge due to soil water infiltration and compared this value with the simulated base flow in the sewer

network.

3.1.2 Pin Sec catchment 20

The Pin Sec experimental site is located in the eastern section of Nantes; it has been a part of the Nantes Observatory for the

Urban Environment (ONEVU) since 2006 and thus contains a dense network of continuous measurement equipment (rain

gauges, flow meters in networks, piezometers, tensiometers and micro-climatological masts). In correspondence with the

simulation period of this study, rainfall patterns were analysed between May 2010 and September 2012, with an annual

rainfall of approx. 700 mm for the year 2011. 25

The catchment area spans 31 ha with some 2,500 inhabitants (Le Delliou et al., 2009). The northern part of the site is

characterised by single-family housing with private gardens, unlike the southern part, which encompasses 4-storey multi-

family buildings with public parks (Fig. 2b). The sewer network is separate, divided into wastewater and stormwater with

respective lengths of 6,973 m and 3,911 m. 51% of the total area is impervious, of which only 61% has been found (survey

conducted by the Nantes Metropolitan government) to be connected to the stormwater sewer. A description of this catchment 30

is summarised in Tab. 1.


9

3.2 Meteorological forcing

Forcing the model with observations requires atmospheric data, such as precipitation, temperature, specific humidity,

atmospheric pressure, wind speed and direction, and incoming shortwave and longwave radiation. For both experimental

sites, the precipitation rates (no snowfall for all simulation periods) were collected on site by means of rain gauges.

All other forcing data were generated from the data of the nearby Météo-France weather station (at Nantes Airport), 5

including incoming solar radiation, cloudiness, pressure, air temperature and humidity at 2 m above ground, and wind speed

at 10 m above ground. To avoid the direct influence of the urban canopy, the forcing level height for temperature, humidity

and wind had to be set above the roughness sublayer top, hence the atmospheric data had to be adjusted accordingly

(Lemonsu et al., 2012).

4. Evaluation of the TEB-Hydro model 10

The TEB-Hydro model was evaluated by comparing the simulated with the observed total sewer discharge and the portion of

this discharge due to soil water infiltration. Observations were derived from the two experimental sites described above.

Let's note that the local properties of these sites, as well as the simulation period, do vary. A sensitivity analysis performed

on the Rezé catchment will be presented first. The hydrological parameters taken into account consist of: the maximum

retention capacity of the artificial surfaces 𝑊𝑚𝑎𝑥,∗𝑠𝑢𝑟𝑓

(roads and buildings), a parameter describing the water-tightness of the 15

sewer pipe 𝐼𝑝 , the maximum infiltration rate through the road structure 𝐼𝑟𝑑 , the fraction of impervious surface areas

connected to the sewer network 𝑓𝑐𝑜𝑛, and the deep drainage 𝐷∗ (Sect. 2 and Tab. 2). In addition, possible combined effects of

these studied parameters will also be analysed. As is typical with hydrological models, the model is calibrated on those

parameters where it shows the greatest sensitivity. Next, the model will be evaluated on the observed total sewer discharge

of both the Rezé and Pin Sec catchments. Simulations will be run with the TEB-Hydro model and then compared to 20

observations in order to discuss the performance of recent model developments.

4.1 Model configuration

The TEB-Hydro model (SURFEX v7.3) has been applied to a single grid point (1D) for both experimental sites; it operates

in "off-line" mode, forced by meteorological observations (Sect. 3.2), with a one-hour time step. The model's numerical time

step is 5 min. For both catchments, 12 soil layers were taken into account, and the road structure was divided into 5 artificial 25

layers. By virtue of the mean sewer system depth (1.50 m), the sewer pipe is thus situated in the 10th soil layer. Natural

surfaces are represented by bare ground, low and high-growth vegetation.

In the case of the Rezé catchment, the model was run over a 6-year period, from January 1993 to December 1998. The

hydrological year starts in September, as the lowest base flow can be detected in August for the Nantes region. Its

morphological data, radiative and thermal properties of the materials (TEB), and soil and vegetation properties (ISBA) have 30

all been considered, like in Lemonsu et al. (2007).


10

The simulation period for the Pin Sec catchment is 2.5 years, i.e. between May 2010 and September 2012. The

morphological site data, radiative and thermal properties of the materials (TEB), and soil and vegetation properties (ISBA)

were determined on the basis of several sources (FluxSAP database (Furusho, 2012), Nantes Metropolitan urban databank,

and Ecoclimap I (Faroux et al., 2013)). Due to inconsistencies between previous studies (Le Delliou et al., 2009; Seveno et

al., 2014), the Pin Sec catchment area has been re-delimited using a GIS (Fig. 2b). 5

4.2 Sensitivity analysis

The sensitivity analysis was solely conducted on the Rezé catchment; its aim was to better understand the role of each

individual parameter on the various hydrological processes and identify those responsible for greater model sensitivity and

thus requiring calibration. In general, two types of analyses were conducted: local and global (Saltelli et al., 2004; Tang et

al., 2006). For this study, a local analysis based on the One Factor at a Time (OFAT) method was chosen (Montgomery, 10

2017). This approach measures the influence of a parameter by the amplitude in variation of the model's response around a

nominal value of this parameter. The sensitivity analysis encompasses several hydrological parameters, with a range of

realistic values (minimum, nominal, maximum). These values have been identified from either a literature review or in situ

measurements (Berthier et al., 1999; Lemonsu et al., 2007; Furusho et al., 2013) (Tab. 2). The REF simulation is based on

the nominal values of all parameters. The MIN and MAX simulations can consistently be performed when a single 15

parameter is changed respectively to its minimum and maximum values, while the other parameters remain fixed at their

nominal values.

Moreover, a two-level factorial plan of 23 is presented in order to determine whether or not some parameters (Ip, Ird and D∗)

display combined effects on the model output and then dissemble the interactions taking place between them. Such a design

is of common use in experiments involving several interlinked factors (Montgomery, 2007). 20

Each parameter is assigned two levels, which serves to limit the experimental domain. In the current case, the domain of

each parameter corresponds to the margins set for the sensitivity analysis. The higher level will hereafter be denoted +1 for

the MAX parameter value and -1 for the lower value corresponding to the parameter MIN value (Tab. 3). To take all

possible parameter combinations into account, a matrix is generated with all values being arranged according to the "Yates

Order". The principal effects (Eq. 17) of the given parameters and the effects of their interactions (Eq. 18) are then 25

calculated, in direct correlation with the mean response of both its low level (�̅�∗−) and high level (�̅�∗+). The dependence of

two parameters can be analysed visually by showing the effects of both parameters on the model response (y̅∗): two perfect

parallel lines would not indicate any interdependence between the two factors, as opposed to non-parallelism.

In the current context, �̅�∗ corresponds to the maximum observed sewer discharge due to soil water infiltration Qsew,max

during winter 1994/95 in the Rezé catchment. A positive effect stands for an increase of this process while transitioning from 30

the low parameter level (-1) (MIN value) to its high value (+1) (MAX value), and vice versa in the case of a negative effect:

𝑒(𝐴) = �̅�𝐴+ − �̅�𝐴− (17)


11

𝑒(𝐴𝐵) = �̅�𝐴𝐵+ − �̅�𝐴𝐵− (18)

where 𝑒(𝐴) is the principal effect of a parameter called 𝐴 , 𝑒(𝐴𝐵) the effect of the interaction between two different

parameters 𝐴 and 𝐵, �̅�∗+ the mean response of all combinations where the parameter or the interaction of two parameters is

at its high level (+1), and �̅�∗− the mean response of all combinations where the parameter or the interaction of two

parameters is at its low level (-1). 5

4.3 Comparative method

In the case of the sensitivity analysis, the Kling-Gupta statistical criterion (KGE) has been calculated from the output

variables of the MIN or MAX simulations as Dsim(t), and from the output variables of the REF simulation as Dref(t) (Eqs. 19

to 22). For the model calibration and evaluation phase, Dref(t) is replaced by observed data Dobsf(t). The Kling-Gupta

efficiency (KGE) coefficient is a synthesis of several criteria varying between 1 and -∞ (Gupta et al., 2009): 10

𝐾𝐺𝐸 = 1 − √(𝑟 − 1)2 + (𝛼 − 1)2 + (𝛽 − 1)2 (19)

With the linear correlation coefficient (r):

𝑟 =∑((𝐷𝑠𝑖𝑚(𝑡)−𝐷𝑠𝑖𝑚̅̅ ̅̅ ̅̅ ̅̅ )∗(𝐷𝑟𝑒𝑓(𝑡)−𝐷𝑟𝑒𝑓̅̅ ̅̅ ̅̅ ̅))

√∑(𝐷𝑠𝑖𝑚(𝑡)−𝐷𝑠𝑖𝑚)̅̅ ̅̅ ̅̅ ̅̅ ̅2∗√∑(𝐷𝑟𝑒𝑓(𝑡)−𝐷𝑟𝑒𝑓)̅̅ ̅̅ ̅̅ ̅̅ ̅2 (20)

With the relative variability (α) represented by the standard deviation:

𝛼 =√∑(𝐷𝑠𝑖𝑚(𝑡)−𝐷𝑠𝑖𝑚)̅̅ ̅̅ ̅̅ ̅̅ ̅2

√∑(𝐷𝑟𝑒𝑓(𝑡)−𝐷𝑟𝑒𝑓)̅̅ ̅̅ ̅̅ ̅̅ ̅2 (21) 15

And the bias (β):

𝛽 =𝐷𝑠𝑖𝑚̅̅ ̅̅ ̅̅ ̅̅

𝐷𝑟𝑒𝑓̅̅ ̅̅ ̅̅ ̅ (22)

The results of the Kling-Gupta efficiency (KGE) criteria are then presented for each MIN and MAX simulation. For this

analysis, the chosen model output variables depend on the influence of the parameter on the hydrological processes, namely:

Urban runoff (𝑅𝑡𝑜𝑤𝑛) and the subsequent total urban discharge (wastewater and stormwater sewer) (𝑄𝑡𝑜𝑤𝑛𝑡𝑜𝑡 ); 20

Soil water drainage via the sewer network (𝑅𝑠𝑒𝑤).

4.4 Calibration

Based on the outcomes of the sensitivity analysis, the model is then calibrated. The first few months of the spin-up

simulation period are systematically excluded in order to anticipate problems upon initialising the model's prognostic

variables. Calibration is applied transversally, meaning that after removing the spin-up time from the simulation period, it is 25

split into two equal periods, and the model is calibrated and evaluated on both of them. By doing so, the model will first be

calibrated on the first period and then evaluated on the second in following the same process by inversing calibration and


12

evaluation periods. The simulations are then compared with the observed total sewer discharge and, like for the sensitivity

analysis (Sect. 4.3), the KGE criterion is calculated along with its components.

5. Results and discussion

5.1 Sensitivity analysis

As shown in Tab. 4, the KGE coefficients for both the MIN and MAX simulations specific to maximum retention capacity of 5

the surface reservoir of roads (Wmax,rdsurf ) and roofs (Wmax,rf

surf ) show little difference for both the urban runoff and runoff due to

soil water infiltration (Figs. 3a and 3b). In the case of maximum roof retention capacity, urban runoff is mainly influenced by

small rainfall events.

In terms of urban runoff, the model does not show any higher sensitivity to the parameter describing the infiltration rate

through the road (Ird) than to Wmax,rdsurf and Wmax,rf

surf (Tab. 4). Such is not the case however when considering the sewer runoff 10

due to soil water infiltration. As the road infiltration rate increases, total surface runoff decreases but only for small rain

events (Fig. 4a). Also, soil moisture rises within the soil layers, thus boosting soil water infiltration into the sewer network

(Fig. 4b).

As expected, the model is more sensitive to the fraction of impervious surfaces connected to the sewer system (𝑓𝑐𝑜𝑛) (Fig. 5).

The bias (β) and relative variability (α) (Tab. 4) reveal different values for MIN and MAX simulations, yet they both lead to 15

the same KGE criterion (Tab. 4). The variation in the fcon parameter influences urban runoff as well as sewer runoff due to

soil water infiltration. A low connection rate leads to a lower urban runoff, while a greater parameter value increases urban

runoff (Fig. 5). The runoff from surfaces not connected to the sewer system feeds the infiltration towards the natural

surfaces. The amount of infiltrated water in the garden compartment thus changes with this parameter, thereby influencing

the soil moisture in all layers and compartments. These values are higher when the fraction of connected surfaces is low and, 20

conversely, lower with a high fraction.

The calculated KGE values (Tab. 4) are quite divergent between the MIN and MAX simulations for parameters 𝐼𝑝 and 𝐷∗

with both output variables, which implies that the model is very sensitive to them. In addition, the results of the factorial plan

(Fig. 6), based on the calculated direct effects on the maximum sewer discharge due to soil water infiltration, corroborate

these results. 25

As for the parameter describing the water-tightness of the sewer pipe (Ip), its increase leads to higher peaks of infiltration

into the sewer network (Fig. 7a) but does not influence the infiltration period. Moreover, the calculated effect of an 𝐼𝑝 of

+2.9E-04 signifies an increase in soil water infiltration into the sewer network when transitioning from its low level (-1) to

its high one (+1) (Fig. 6). In fact, soil water drainage via the sewer network is as important as a degraded network condition

(cracks, root penetration, etc.), and soil moisture at the network location is close to saturation. 30


13

As for the deep drainage parameter (𝐷∗), the negative effect (Fig. 6) indicates that infiltration declines with an increasing

parameter value. As seen in Fig. 7b, limiting deep drainage to a magnitude of 10% (MAX) does not generate a significant

difference with the reference simulation in assessing sewer discharge due to soil water infiltration. Blocking the deep

drainage completely (MIN) however leads to a saturation of the lower soil layers, thus adding to the soil water infiltration

into the sewer network (Fig. 7b). 5

As was the case for water-tightness of the sewer pipe (𝐼𝑝), both the infiltration rate through the road (𝐼𝑟𝑑) and deep drainage

(𝐷∗) seem to influence the sewer drainage due to soil water infiltration, with the effects of their interactions having been

calculated and visualised. In this manner, the 𝐼𝑝/𝐷∗ interaction can be highlighted as the most influential of all three first-

order interactions (Fig. 6). In addition, Figure 8 effectively shows the correlation between the two parameters (see the two

lines run non-parallel to one another), whereas the correlations between the other parameters appear to be less significant. 10

In comparing model sensitivity among the 6 parameters for both urban runoff and runoff due to soil water infiltration, it can

be concluded that the model is less sensitive to changes in parameters Wmax,rdsurf and Wmax,rf

surf . Four parameters can thus be

singled out for calibration:

The parameter describing the water-tightness of the sewer pipe (𝐼𝑝)

Infiltration rate through the road (𝐼𝑟𝑑) 15

The fraction of impervious surfaces connected to the sewer network (𝑓𝑐𝑜𝑛)

Deep drainage (𝐷∗).

5.2 Model calibration and evaluation

In considering the results of the sensitivity analysis, this model needs to be calibrated on four parameters. Yet for both

catchment areas, the parameter 𝑓𝑐𝑜𝑛 has been determined during exhaustive field surveys and therefore is well known. 20

Consequently, this parameter will be neglected, hence only the three remaining parameters are considered for calibration.

Four different values within the predefined range of the sensitivity analysis are tested for each parameter (Tab. 5). The model

is calibrated and evaluated on the total observed sewer discharge (𝑄𝑡𝑜𝑤𝑛𝑡𝑜𝑡 ), as determined from the model outcome variable:

urban runoff (𝑅𝑡𝑜𝑤𝑛). However, since the drainage capacity of soil water through the sewer network can be extensive in

urban areas, the share of sewer discharge originating from soil water infiltration (𝑄𝑠𝑒𝑤) has been investigated in detail. 25

Hence, the choice of this parameter's values also depends on the findings of the sensitivity analysis with respect to this

output variable (𝑄𝑠𝑒𝑤). In Section 5.1, it was shown that soil water infiltration into the sewer increases as the 𝐼𝑝 value rises,

as opposed to parameters 𝐼𝑟𝑑 and 𝐷∗. The range of values has thus been set close to the maximum 𝐼𝑝 value and minimum 𝐼𝑟𝑑

and 𝐷∗ values. Totally blocking the deep drainage however is not an option, since in reality soil water is not only drained by

artificial sewer systems but moreover can find other pathways within the urban subsoil (groundwater recharge, seepage, 30

etc.).


14

5.2.1 Rezé catchment

In the Rezé catchment, the calibration and evaluation periods have been compounded by two consecutive hydrological years,

i.e. from September 1993 to August 1995, and from September 1995 to August 1997.

The KGE criterion results indicate a clear and constant trend for all simulations, independently of the considered time period

(Fig. 9) or the value of parameter D∗: 5

For starters, as seen in the example (deep drainage limited to 2%), all KGE criteria are far better for the first period from

1993 to 1995 than for the second (1995-97) (Fig. 9). This discrepancy between the two simulation periods is primarily

related to the KGE criterion component bias (β), which shows a greater bias for the second simulation period (Fig. 9).

Secondly, the smallest value of Ip achieves a better result than the highest value, when assessing total sewer discharge.

Thirdly, the parameter Ird does not exert significant influence on the simulated total sewer discharge, since the criterion does 10

not vary much among its different values.

The correlation (r) of simulated and observed discharge peaks is satisfactory, with values of about 0.90 for both simulation

periods and all simulation configurations (Fig. 9). The model displays a tendency to overestimate the observed total sewer

discharge (Fig. 10), more so for the second simulation period, showing greater variability (α) through all simulations (Fig. 9).

Regardless of the deep drainage values, simulation 13 seems to stand out with a KGE between 0.79 and 0.82 over the entire 15

simulation period. The KGE values range between 0.81 and 0.84 for the first period and between 0.66 and 0.68 for the

second. In examining both simulation periods separately, simulation 14 seems to perform slightly better for the first period.

Given the fact that simulation 13 performs much better over the second period than simulation 14, simulation 13 should also

be tagged for a transversal calibration. The degradation in KGE during the second year is mainly related to the higher bias

values, most likely caused by the various hydrological properties of both simulation periods. For the first period 1993-95, a 20

total precipitation height of approx. 1,873 mm with a very wet winter during 1994-95 can be observed, whereas the second

period is much dryer posting just 1,302 mm.

As regards total sewer discharge, the best combination of parameters would be to set parameter Ip at 0.09 and Ird at 10-5,

whereas parameter D∗ can vary. We will thus be examining in greater detail the portion of sewer discharge due to soil water

infiltration, with parameter D∗ influencing this process significantly. Berthier (1999) observed a maximum sewer discharge 25

due to soil water infiltration of about 0.008 m3 h-1 lm-1 during the winter 1994-95. Accounting for the total sewer length of

1,283 m at the Rezé catchment would yield a maximum sewer infiltration rate of roughly 10.3 m3 h-1. Limiting deep drainage

to 2% produces (Fig. 11a) a simulated discharge peak of 4.8 m3 h-1 during this period, which is much less than observation

findings. In looking at the simulation with a limited deep drainage (D∗) of 1%, the observed discharge peak becomes

significantly overestimated at 27 m3 h-1 (Fig. 11b). In the aim of evaluating the model as well on the sewer discharge due to 30

soil water infiltration, deep drainage should be limited somewhere between 1% and 2%.

Another option would consist of focusing on the Ip parameter since the sensitivity analysis also revealed its influence on the

process of soil water infiltration into the sewer. As stated above, raising the value of Ip is beneficial for the infiltration rate.


15

Hence, simulation 14 would be more suitable, as Ip has been set at 0.3 while Ird remains at 10-5. In conjunction with deep

drainage limited to 2%, the maximum sewer discharge due to soil water infiltration during winter 1994-95 equals roughly

10.6 m3 h-1, which is close to the observed discharge (Fig. 11c). For this combination of parameters (i.e. Ip =0.3, Ird=10-5,

D∗=2), the KGE criterion based on total sewer discharge is slightly better, like for simulation 13, with a value of 0.86 for the

first period. Such is not the case however for the second period, with a value of 0.57. 5

5.2.2 Pin Sec catchment

For the Pin Sec catchment, the period between September 2010 and August 2011 has been compared to the period from

September 2011 to August 2012 and vice versa.

As was the case with the Rezé catchment, the same trends and tendencies can be observed independently of the simulation

periods and configurations. Simulation 13 can once again be cited as the best configuration of parameters, with a KGE 10

criterion of 0.79 over the whole simulation period. Parameter Ip can thus be set at 0.09 and Ird at 10-5, whereas D∗ is variable.

5.2.3 General discussion

In terms of calibration and evaluation processes, this model exhibits the tendency to overestimate the observed total sewer

discharge. This skewing can be explained by the choice of setting parameter 𝑓𝑐𝑜𝑛 at its real value rather than calibrating the

model on it. This parameter is indeed the one exerting a predominant influence on total sewer discharge, since it directly 15

conditions the surface runoff of impervious surfaces. When calibrating the model on total sewer discharge, it is thus essential

to take this parameter into account in case it is not well known, as opposed to other parameters 𝐼𝑟𝑑 and 𝐷∗ that exercise little

influence over this process. Evaluating the model from the standpoint of sewer discharge due to soil water infiltration

however requires a more detailed consideration of 𝐼𝑝 and 𝐷∗. The water exchanges taking place between the urban subsoil

and both the natural and sewer network are critical processes in urban areas. As shown above, the model is very sensitive to 20

them and comparing them to observation findings can help improve the simulated urban water budget, yet experimental data

on such fluxes are indeed rare.

For both catchments, the statistical criteria indicate the same trend throughout all simulation configurations and periods, with

a better KGE for the first period. The model seems to perform better under wetter climatic conditions. The best simulation

configuration is the same irrespective of calibrating the model on the first or second period, with the exception of Simulation 25

14. It thus proves necessary to apply the model more extensively in regions with different meteorological patterns in order to

investigate whether the model could operate under different meteorological conditions (dry and wet periods), which is an

essential condition for projection applications. The same simulation configuration yields the best results for both the Rezé

and Pin Sec catchments. Considering their differences in terms of soil texture and urban patterns (mean building height), this

is an encouraging result for working at the city scale, as spatial heterogeneity no longer constitutes an obstacle. 30


16

6. Conclusion

The objective of this study has been to contribute to developing a complete urban hydro-microclimate model and testing the

ability of this model to replicate hydrological processes. This goal has been achieved given that the representation of

hydrological processes in the TEB-Veg model (Lemonsu et al., 2012) has been extended and refined. The new model

version, called TEB-Hydro, has been developed by taking a detailed representation of the urban subsoil into account. This 5

step has enabled horizontal interactions of soil moisture between the urban subsoil of built-up and natural surfaces within a

single grid-cell. Furthermore, the drainage of soil water via the sewer network has been introduced in the road compartment

of the model. Deep drainage, which normally supplies the base flow of the natural river network, has been limited to

favouring humidification of the lower soil layers, resulting in more realistic infiltration patterns into the sewer network under

urban conditions. A sensitivity analysis has been performed in the aim of better understanding the influences of model 10

parameters on these processes and identifying the parameters to serve calibration purposes. Six parameters were

investigated, of which four seemed to significantly influence the model output in terms of total sewer discharge and the

portion of discharge caused by soil water infiltration, namely: the parameter (𝐼𝑝) describing the water-tightness of the sewer

pipe, the road infiltration rate (𝐼𝑟𝑑), the fraction of impervious surfaces connected to the sewer network (𝑓𝑐𝑜𝑛), and the

parameter (𝐷∗) that enables limiting deep drainage out of the urban subsoil. 15

TEB-Hydro was then applied to two small residential catchments located close to the city of Nantes (France). In both cases,

the model was calibrated and evaluated on the observed sewer discharge, in displaying the same hydrological behaviour. The

total sewer discharge is consistently being overestimated, independent of both simulation period and configuration.

Considering parameter 𝑓𝑐𝑜𝑛 as a calibration element, should it not be known, allows tackling this problem. The model seems

to function better under wet conditions, since simulation period 1 offers better KGE results. In assessing the entire simulation 20

periods for both catchments, the same parameter configuration stands out, independently of meteorological and local

physical conditions, thus implying that the model is running in a coherent and steady manner. This finding would need to be

confirmed by applying the model to several catchments areas outside of Nantes. In conclusion, the evaluation outcomes laid

out herein are encouraging for application of the model at the city scale for purposes of projecting global change.

Lastly, a more detailed representation of the urban subsoil and its hydrological pattern enhances the model's urban water 25

budget. Given that the water and energy budgets are coupled, it is likely that the energy budget of the model is improved at

the same time. An upcoming research project is underway, which entails investigating alongside the hydrological processes

energy patterns like latent and sensible heat fluxes.

7. Code and data availability

The surface modelling platform SURFEX is accessible on open source, where the codes of surface schemes TEB and ISBA 30

can be downloaded (http://www.cnrm-game-meteo.fr/surfex/). This platform is regularly updated; however, the model


17

developments mentioned above have yet to be taken into account in the latest SURFEX, version v8.0. For all further

information or access to real-time code modifications, please follow the procedure in order to open the SVN account

provided via the previous link. The routines modified with respect to the TEB-Hydro model SURFEX v.7.3, as well as the

run directories of the model experiments described above can be retrieved via https://doi.org/10.5281/zenodo.1218016. The

Rezé and Pin Sec catchment databases are available upon request submitted to the authors of the Water and Environment 5

Laboratory of the French Institute of Science and Technology for Transport, Development and Networks (IFSTTAR).

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21

Table 1: Summary of basin characteristics for both the Rezé and Pin Sec catchments

Description Rezé Pin Sec

Surface area 4.7 ha 31.3 ha

Housing type Residential

(individual)

Residential

(individual and multi)

Mean building height (Hmean) 5.9 m 9.3 m

garden

Land use building

road

55%

17%

28%

49%

19%

32%

Soil texture clay

sand

40%

38%

8%

51%

Imperviousness of the surface area 45% 51%

Impervious surfaces connected to the sewer 84% 61%

Length of sewer network wastewater

storm drain

803 m

480 m

3,911 m

6,972 m

Mean sewer depth 1.50 m 1.50 m

Table 2: Description of the hydrological parameters of the TEB-Hydro model as well as its MIN, MAX and REF values for the

sensitivity analysis 5

Simulation Parameter Description Unit Values

MIN REF MAX

SROAD 𝑊𝑚𝑎𝑥,𝑟𝑑𝑠𝑢𝑟𝑓

Maximum retention capacity of the road

surface reservoir mm 0.5 3.0 6.0

SROOF 𝑊𝑚𝑎𝑥,𝑟𝑓𝑠𝑢𝑟𝑓

Maximum retention capacity of the roof

surface reservoir mm 0.25 1.5 3.0

IP 𝐼𝑝 Parameter that describes the water-tightness

of the sewer pipe - 10-3 10-1 1

IROAD 𝐼𝑟𝑑 Infiltration rate through the road mm s-1 10-9 10-6 10-5

CONN 𝑓𝑐𝑜𝑛 Fraction of impervious surfaces connected to

the sewer network - 0.5 0.7 0.9

DRAIN 𝐷∗ Deep drainage % 0 5 10


22

Table 3: All factors with their levels and assigned values according to the sensitivity analysis classification

Parameter Level -1 Level +1

𝑰𝒑 10-3 1

𝑰𝒓𝒅 10-9 10-4

𝑫∗ 0 10

Table 4: Statistical criteria (r, α, β, KGE) based on the model output variables, as calculated between the MIN and MAX

simulations, of each parameter and the reference simulation (REF)

Output variable Simulation MIN criteria MAX criteria

r α β KGE r α β KGE

𝑄𝑡𝑜𝑤𝑛𝑡𝑜𝑡

SROOF 1.00 1.01 1.06 0.94 1.00 0.99 0.96 0.96

SROAD 0.99 1.04 1.11 0.88 0.99 0.96 0.94 0.93

IROAD 1.00 1.00 1.01 0.99 1.00 0.98 0.94 0.94

CONN 1.00 0.73 0.75 0.64 1.00 1.28 1.25 0.63

IP 1.00 1.00 0.93 0.93 1.00 1.01 1.41 0.59

DRAIN 0.91 1.20 1.80 0.17 1.00 1.00 0.99 0.99

𝑄𝑠𝑒𝑤

SROOF 1.00 1.01 1.06 0.94 1.00 0.99 0.96 0.96

SROAD 0.99 1.04 1.11 0.88 0.99 0.96 0.94 0.93

IROAD 1.00 0.99 0.99 0.98 1.00 1.05 1.09 0.90

CONN 0.99 1.19 1.21 0.72 0.98 0.82 0.78 0.72

IP 1.00 0.01 0.01 -0.40 0.99 7.43 7.0 -7.79

DRAIN 0.78 20.51 11.47 -21.14 1.00 0.90 0.84 0.81

5

Table 5: Range of values for each parameter tested for use in calibration

𝐼𝑝[-] 0.09 0.3 0.6 1

𝐼𝑟𝑑[mm s-1] 10-8 10-7 10-6 10-5

𝐷∗[%] 1 2 3.5 5


23

Figure 1: Schema of the hydrological processes involved in the TEB-Hydro model; subscripts rf and bld stand for building

compartment, rd for road compartment, and gdn for garden compartment

Figure 2: a) the experimental Rezé site (from Dupont, 2001); b) the experimental Pin Sec site. Maps to the right of the catchments 5 indicate the location of Nantes (France) above and the Rezé and Pin Sec catchment locations (red square) in Nantes (middle)


24

Figure 3: Comparison of urban runoff (𝑹𝒕𝒐𝒘𝒏) between the reference simulation (REF) and both the MIN simulation (shown in

blue) and MAX simulation (red) for the parameters: a) 𝑾𝒎𝒂𝒙,𝒓𝒅𝒔𝒖𝒓𝒇

(left side), and b) 𝑾𝒎𝒂𝒙,𝒓𝒇𝒔𝒖𝒓𝒇

(right side).

5

Figure 4: a) Comparison of urban runoff (𝑹𝒕𝒐𝒘𝒏) between the reference simulation (REF) and both the MIN simulation (blue) and

MAX simulation (red) for parameter 𝑰𝒓𝒅 on the left side; and b) comparison of the sewer runoff due to soil water infiltration

(𝑹𝒔𝒆𝒘) between the reference simulation (REF) and the MIN (blue) and MAX (red) simulations for parameter 𝑰𝒓𝒅 on the right side


25

Figure 5: Comparison of urban runoff (𝑹𝒕𝒐𝒘𝒏) between the reference simulation (REF) and the MIN (blue) and MAX (red)

simulations for parameter 𝐟𝐜𝐨𝐧

Figure 6: Calculated effects on the model response (𝑹𝒔𝒆𝒘) of parameters 𝑰𝒑, 𝑰𝒓𝒅 and 𝑫∗ and their interactions. (dark shade of 5

grey: principal effects, middle grey: second-order effects, and light grey: third-order effects)

IP

IROAD

DRAIN

IP/IROAD

IP/DRAIN

IROAD/DRAIN

IP/IROAD/DRAIN

-3,0E-04

-2,0E-04

-1,0E-04

0,0E+00

1,0E-04

2,0E-04

3,0E-04

4,0E-04

e(*

)


26

Figure 7: Comparison of sewer runoff due to soil water infiltration (𝑹𝒔𝒆𝒘) between the reference simulation (REF) and the MIN

(blue) and MAX (red) simulations for parameters a) 𝑰𝒑 (left side) and b) 𝑫∗ (right side)

Figure 8: Interactions as a function of the maximum observed sewer runoff due to soil water infiltration during winter 1994-95 of 5 the second order between parameters: a) 𝑰𝒑 and 𝑰𝒓𝒅; b) 𝑰𝒑 and 𝑫∗ and of third order between parameters c) 𝑰𝒑, 𝑰𝒓𝒅 and 𝑫∗

0,0E+00

5,0E-05

1,0E-04

1,5E-04

2,0E-04

2,5E-04

3,0E-04

3,5E-04

-1 0 1

Qm

ax

IP

a) IP/IROAD

IROAD (+1)

IROAD (-1)

0,0E+00

1,0E-04

2,0E-04

3,0E-04

4,0E-04

5,0E-04

-1 0 1

Qm

ax

IP

b) IP/DRAIN

DRAIN (+1)

DRAIN (-1)

0,0E+00

5,0E-05

1,0E-04

1,5E-04

2,0E-04

2,5E-04

3,0E-04

-1 0 1

Qm

ax

IROAD

c) IROAD/DRAIN

DRAIN (+1)

DRAIN (-1)


27

Simulations 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

𝐼𝑝 0.09 0.3 0.6 1 0.09 0.3 0.6 1 0.09 0.3 0.6 1 0.09 0.3 0.6 1

𝐼𝑟𝑑 10-8 10-8 10-8 10-8 10-7 10-7 10-7 10-7 10-6 10-6 10-6 10-6 10-5 10-5 10-5 10-5

𝐷∗ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

Figure 9: Example of a calculated criterion for the simulation configurations where parameter 𝐃∗ (deep drainage) is limited to 2% 5 and all other parameters allowed to vary. The KGE criterion, the correlation criterion (r), the variability criterion (α) and the bias

(β) for all 16 simulations and for the first (dark grey) and second (light grey) simulation periods are shown.

0,00

0,20

0,40

0,60

0,80

1,00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

KG

E

Period 1 Period 2

0,80

0,85

0,90

0,95

1,00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

r

1,00

1,10

1,20

1,30

1,40

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

α

0,80

1,00

1,20

1,40

1,60

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

β

Simulations


28

Figure 10: Comparison of simulated and observed total sewer discharge [l s-1] during: a) the first simulation period from

September 1993 to August 1995 (left side); and b) the second simulation period from September 1995 to August 1997 (right side)

for Simulation 13 and a deep drainage limited to 2%

5

Figure 11: Simulated sewer discharge due to soil water infiltration during the first simulation period 1993-95 based on the

combination of parameters 𝐈𝐩 set at 0.09 and 𝐈𝐫𝐝 set at 10-5 and: a) 𝐃∗ limited to 2%, b) 𝐃∗ limited to 1%, and c) based on the

combination of parameters 𝐈𝐩 set at 0.3, 𝐈𝐫𝐝 set at 10-5, with 𝐃∗ limited to 2%


improvements of the hydrological processes of the town

Documents